If the starting point is not today, you could say: "From that day onward" or "From that day forward" If the day you're referencing is today (more likely), you would say: "From this day onward" or "From this day forward" In either case, either option is correct and you would be understood, but we would normally use "forward" rather than "onward".

Yes, because "onward/onwards" and "forward" are all synonyms.